jmc

Bob is equally likely to end up rolling a 2, 3, 4, 5, or 6. Three of these numbers are prime and two are composite, so there is a $\frac{3}{5}$ chance he will eat unsweetened cereal and a $\frac{2}{5}$ chance that he will eat sweetened cereal. In a non-leap year, there are 365 days, so the expected value of the number of days Bob eats unsweetened cereal is $\frac{3}{5}\cdot 365=219$ and the expected value of the number of days Bob eats sweetened cereal is $\frac{2}{5}\cdot 365=146$. The difference between 219 days and 146 days is $\boxed{73}$ days.